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Write a quadratic function f whose only zero is -12 .

Write a quadratic function ff whose only zero is −12-12.

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Full solution

Q. Write a quadratic function ff whose only zero is −12-12.
  1. Identify Zero and Factor: Identify the zero and the corresponding linear factor.\newlineSince −12-12 is the only zero, the linear factor is (x+12)(x + 12). Since it's the only zero, it must be a double root.
  2. Write Quadratic Function: Write the quadratic function using the double root.\newlineThe quadratic function is f(x)=(x+12)2f(x) = (x + 12)^2.
  3. Expand Quadratic Function: Expand the quadratic function.\newlineUsing the formula (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2, expand (x+12)2(x + 12)^2.\newlinef(x)=(x+12)2=x2+24x+144f(x) = (x + 12)^2 = x^2 + 24x + 144.

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